About half of the cuts will be in the U.S. Morgan Stanley's investment banking unit has been asked to cut about 6 percent of its staff. Back-office functions, including human resources and communications, have also been asked to cut staff. The person familiar with the matter wasn't authorized to speak on the record and insisted on remaining anonymous.

Job cuts have become common in the banking industry, which has been shrinking in the years since the financial crisis imploded.

In December, Citigroup said it would cut 11,000 jobs, about 4 percent of its total workforce, and Bank of America has also been trimming jobs.